|
%I #13 Jan 04 2018 07:40:57
%S 1,2,14,92,844,9304,121288,1822736,31030928,590248736,12406395616,
%T 285558273472,7143371664064,192972180052352,5598713198048384,
%U 173627942889668864,5731684010612723968,200669613102747214336,7426773564495661485568,289713958515451427511296
%N Number of maximal matchings in the n-cocktail party graph.
%C A maximal matching in the n-cocktail party graph is either a perfect matching or a matching with a single unmatched pair. - _Andrew Howroyd_, Dec 30 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CocktailPartyGraph.html">Cocktail Party Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>
%F a(n) = A053871(n) + n*A053871(n-1). - _Andrew Howroyd_, Dec 30 2017
%t Table[(-1)^(n + 1) (n HypergeometricPFQ[{1/2, 1 - n}, {}, 2] - HypergeometricPFQ[{1/2, -n}, {}, 2]), {n, 20}]
%t Table[-I (-1)^n (n HypergeometricU[1/2, n + 1/2, -1/2] - HypergeometricU[1/2, n + 3/2, -1/2])/Sqrt[2], {n, 20}]
%o (PARI) \\ here b(n) is A053871.
%o b(n)={if(n<1, n==0, sum(k=0, n, (-1)^(n-k)*binomial(n,k)*(2*k)!/(2^k*k!)))}
%o a(n)=b(n) + n*b(n-1); \\ _Andrew Howroyd_, Dec 30 2017
%Y Cf. A053871.
%K nonn
%O 1,2
%A _Eric W. Weisstein_, Dec 30 2017
%E a(9)-a(20) from _Andrew Howroyd_, Dec 30 2017
|
